Astronomy Without A Telescope – Plausibility Check

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So we all know this story. Uncle Owen has just emotionally blackmailed you into putting off your application to the academy for another year – and even after you just got those two new droids, darn it. So you stare mournfully at the setting binary suns and…

Hang on, they look a lot like G type stars – and if so, their roughly 0.5 degree angular diameters in the sky suggest they are both only around 1 astronomical unit away. I mean OK, you could plausibly have a close red dwarf and a distant blue giant having identical apparent diameters, but surely they would look substantially different, both in color and brightness.

So if those two suns are about the same size and at about the same distance away, then you must be standing on a circumbinary planet that encompasses both stars in one orbit.

To allow a stable circumbinary orbit – either a planet has to be very distant from the binary stars – so that they essentially act as a single center of mass – or the two stars have to be really close together – so that they essentially act as a single center of mass. It’s unlikely a planet could maintain a stable orbit around a binary system where it is exposed to pulses of gravitational force, as first one star passes close by, then the other passes close by.

Anyhow, if you can stand on a planet and watch a binary sunset – and you are a water-solvent based life form – then your planet is within the star system’s habitable zone where H2O can exist in a fluid state. Given this – and their apparent size and proximity to each other, it’s most likely that you orbit two stars that are really close together.

To get a planet in a habitable zone around a binary system - your choices are probably limited to circumbinary planets around two close binaries - or circumstellar planets around one star in a widely spread binary. Credit: NASA/JPL.

But, taking this further – if we accept that there are two G type stars in the sky, then it’s unlikely that your planet is exactly one astronomical unit from them – since the presence of two equivalent stars in the sky should roughly double the stellar flux you would get from one. And it’s not a simple matter of doubling the distance to halve the stellar flux. Doubling the distance will halve the apparent diameters of the stars in the sky, but an inverse square relation applies to their brightness and their solar flux, so at double the distance you would only get a quarter of their stellar flux. So, something like the square root of two, that is about 1.4 astronomical units away from the stars, might be about right.

However, this means the stars now need a larger than solar diameter to create the same apparent size that they have in the sky – which means they must have more mass – which will put them into a more intense spectral class. For example, Sirius A has 1.7 times the diameter of the Sun, roughly twice its mass – and consequently about 25 times its absolute luminosity. So even at 2 astronomical units distance, Sirius A would be nearly five times as bright and deliver five times as much stellar flux as the Sun does to Earth (or ten times if there are two such stars in the sky).

So, to sum up…

It’s a struggle to come up with a scenario where you could have two stars in the sky, with the same apparent diameter, color and brightness – unless you are in a circumbinary orbit around two equivalent stars. There’s no reason to doubt that a planet could maintain a stable circumbinary orbit around two equivalent stars, that might be G type Sun analogues or whatever. However, it’s a struggle to come up with a plausible scenario where those stars could have the angular diameter in the sky that they appear to have, while still having your planet in the system’s habitable zone.

I mean OK you’re on a desert world, but two stars of a more intense spectral class than G would probably blow away the atmosphere – and even two G type stars would give you a Venus scenario (which receives roughly double the solar flux that Earth does, being 28% closer to the Sun). They could be smaller K or M class stars, but then they should be redder than they appear to be – and your planet would need to be closer in, towards that range where it’s unlikely your planet could retain a stable orbit.

Like this:

34 Replies to “Astronomy Without A Telescope – Plausibility Check”

How do we know their apparent diameter? This depends on the lens used to shoot the movie.. (ahem, sorry, documentary…) We all know that if you photograph a human model from a far using a telephoto, the background moon or sunsetting sun would look absolutely huge – and vice versa with a wide-angle lens – and so the stellar-size objection is not really solid.

Regarding circumbinary orbits – couldn’t a stable solution be found if there’s an integer resonant relation between the orbital period of the star-pair and the plant? In that case the planetary orbit would actually be a slightly wavy ellipse.

Finally, who said the planet orbits in the plane of the stellar orbit? How much do we know about the evolution of binary systems? Maybe the planet had a close encounter with another planet some 4 Billion years ago and both planets got swung way out of the ecliptic plane? Maybe the planet is actually stellar-bi-polar? (ha!)

So I don’t think the orbital stability issue is that serious. unlikely? maybe. impossible? not so much.

In my next post, I will proceed to explain light sabers, the Force ™, and maybe even that hovering dune-buggy vehicle thing.

Sorry CrazyEddieBlogger. You’ve missed the whole point of the “practical joke” here. The argument expressed here is about thought processes and potentiality, and not just on the actualities.

As for this scenario here, my considered questions would be;

★ If it were a close double star 1AU away, the separation as shown, the two stars would not appear round, but more distorted or teardrop in shape, due to their mutual gravities. This would have a dramatic effect on the photospheres of the stars, made worse by any stellar rotation. What of the coronas of these stars, which being so close they would actually interact?
★ What perturbations would exist with the planet’s orbit? (Consider the small long-term changes on Earth, such as the elliptical orbit of the Earth around the sun, the tilt of the Earth’s axis, the variations in distance from the sun (semi-major axis), etc., and the dramatic effects it has on Earth’s climate — like ice ages.) In a double star system. it would quite dramatically affect the climate and probably even the planet geologically.)
★ In Star Wars example, Tattooine also has two small moons. How stable would their orbits be in a close double star system?
★ Where is the best place to live on planet like this orbiting a double star?
★ How would you describe day and night, especially above the mid-latitudes of the planet? I.e. When one sun or two suns are above or below the planet.
★ What would your shadows look like during the day?

Oh, it’s all tongue in cheek – In my book Star Wars doesn’t clear the minimum threshold for “Science Fiction worth examining for scientific accuracy” – it’s got Ewok’s for crying out loud…. Shall we consider the biologoical probability of Java the Hut or Jar Jar? I’d like analyzing the flight dynamics of Dumbo. 🙂

However, if we’re going to look at the astronomical likelihood of Tatooine, let’s do it properly. The article says ” their roughly 0.5 degree angular diameters in the sky suggest…” and I was pointing out that we can’t tell the 0.5 degree number from looking at the picture, since the camera lens is unknown. (Am I wrong? I am not a photographer…)

There was also an argument about the stability scenarios of a planet around two stars, and I wasn’t sure the argument was well made – I thought that in the general co-planar case such an orbit was unstable, but there were some special cases where it worked. Again, I’m not 100% sure about that.

Actually, this is not “tongue in cheek” at all nor about probabilities. It is mostly a thought experiments to consider the limits of feasibility of some scenarios. (No one, including me, is having a go at you either.)

Your are quite correct to say that imaging through the camera might give a false impression. However, the 0.5° is probably a good theoretical guess, as assuming the planet orbits around both stars, means the habitat zone is around 1 AU. (The 0.5°, of course, being about the current apparent diameter of the Sun from Earth.)
[Comment: Also the end of Episode III, there is a wide image of the setting suns from Tatooine. It seems George Lucas means to infer they are solar-like stars. From the angle of the double star system setting, and assuming the axis of the planet isn’t highly tilted, one could assume the orbit of the planet is aligned roughly to the orbit of the binary system.]

Also with twice the energy emitted by the stars, might account for a more desert-like world. Again doing the thought experiment, if the apparent diameter was more like 0.35#176; to 0.4°, the habitable zone at about 1.3 AU would be about the same energy received by a theoretical Earth-like planet.

Your point about the co-planar orbit is well taken, but we have no way of knowing which way Tatooine is moving. (It is irrelevant in this thought experiment, as all we are considering is the general constraints of meeting the basic scenario. I.e. The possibility of two solar-like stars being orbited by a planet at about 1AU.) Interestingly, the orbital stability would make the orbit more eccentric and subject to perturbation in about 35% of cases, depending on the distance (actually the ratio) from the binary and the distance from the centre of gravity between the two stars. Theoretically,the worst case is roughly 8:1, best is about 500:1. In this 8:1 scenario, if the distance to the two stars is 1 AU, the consequential separation of the two stars at 0.12 to 0.13 AU (18.5 million kilometres, centre to centre, or 17 million kilometres photosphere to photosphere. [c.14 stellar diameters]), would be a serious problem.
In the film, the stars appear about four to five stellar diameters apart, which if true, would mean the shapes of the stars would have to be ellipsoidal not round.
In the end what all this means is really the main question here. Under what limited scenarios could habitable planets exist around binary stars? It also goes on the broader limitation of how planets can form in binary systems; including the overall circumstances of their formation and stability.) Note: Forming binaries is a cinch compared to having stable circumbinary disks sticking around long enough to form stable planets.

Don’t be at all discouraged from having an open mind or considering other possibilities. You might be surprised what you end up finding!
Cheers

So if I’m following correctly:
– We’re both assuming the stars are roughly sol like based on color, but there’s still a good uncertainty on their absolute size. (some +/-30% on the diameter)
– We agree that we can only very roughly judge their apparent size (assuming a normal range of camera lenses) so there’s an added level of uncertainty (~+/- 50%) as to the distance of the planet from the suns.
– This combined uncertainty is enough to allow a planet to orbit the pair without being over-cooked.

So the scenario is not out-right impossible from a purely orbital mechanics point of view. That’s all I was trying to say. I agree about the other points, and am curious about the tear-drop effect you mentioned, and how visible it would be. It would make a beautiful effect…

Star wars was the first movie I’ve ever seen, and practically nobody in the audience has even considered the possibility of “other types” of planets, not to mention visualized it so vividly. This was one of the movie’s high points IMO.

“Finally, who said the planet orbits in the plane of the stellar orbit?”
I don’t think anyone did. The diagram is just a schematic to get a particular point across (if that’s what you mean). Otherwise, I agree the universe keeps surprising us with unexpected stellar system scenarios (e.g. the recent Kepler findings). Perhaps orbital stability is an issue if you are you looking for a planet where life might develop.

Thanks Steve for this entertaining free science lesson.
The plausibility test or check is one of the important tenants when doing any kind of science, which non-scientists and novices often fail to grasp when talking about the common observable phenomena. We often see this in silly arguments such as notions of the “electric universe”, black holes and the cosmology, where totally unsubstantiated claims of new ‘personal’ theories fall flat because they have not considered the actual plausibility of their own arguments.
In science this criteria is often expressed in error analysis, which is in fact just as important as value quoted. Not only does it set limits on the possible range of values for a given measurement, it sets the criteria on the possible variance and validity of good theory. Plausibility, when logically argued, points out possible flaws in the theory, leading to refinement of better or more exact experimentation, and/or better theories.
It is also a very useful tool to sort out fallacious beliefs, where having scepticism of everything thing your read comes second as nature; assessing the likelihood if something is likely true or likely false. An experienced person, when trained in the art, can cut swathes out of wrongly thought out ideas or faulty reasoning. Used concurrently with the other useful tool of Occam’s Razor, 95% of the nonsense in this world would simply vaporise. If only such useful concepts were drilled into people at an early age via the education system, pseudoscience and superstitions may not be such a problem as it is today.

I openly applaud you for this nicely considered article.

Cheers

Note: IMO, especially in blog sites like this one, the “plausibility check” could be a good method of moderation. Frankly, if it doesn’t pass the “idiot test”, it should be removed if only to save confusion by others who know no better.

@ Hon. Salacious B. Crumb – Re: “. If only such useful concepts were drilled into people at an early age via the education system, pseudoscience and superstitions may not be such a problem as it is today.”
…
Hear hear

On a complete side-note, the top picture looks fairly similar to something I saw one afternoon while living in Arizona. I looked above the horizon(around 4 pm), and there were two suns, on the same plane rather than one higher than the other. After studying it a bit, I figured it was some sort of reflection going on with the clouds or moisture at a high level. Nonetheless, it looked very cool.

Good point. George Lucas only made the dual suns for the dramatic emotional effect, hitting home the alien nature of the epic story.
The phenomena you observed is called a mock sun or sundog, and has been known to other observers. Your deduction you make seems valid.
A nice image of one appears in Wikipedia at; http://en.wikipedia.org/wiki/File:Sundog_-KIDWELLY_2010_SUNSET.jpg

Looking at the picture of the Tattooine sunset (http://www.miez.nl/tattoine_2071.jpg) the suns do appear to have the same apparent diameter. But they are definitely not the same color (temperature). Or can we put this down to one of them shining through more atmosphere (being lower towards the horizon)?

Yes – I think it’s reasonable to expect back-scattering of shorter wavelengths when the star is shining through more atmosphere near the horizon – i.e. only red light gets through when it’s near the horizon even though it appears as a white sun higher in the sky.

Image 1) Appears in the original inclined at 30&176; to the horizon and about 1.5 diameters apart.

….then twelve seconds later

Image 2) Shows the wider shot, with the stars inclined at 45° to the horizon and about three diameters apart. These stars appear round, when in the earlier image moments before Image 1 they appear ellipsoidal almost like Jupiter in shape.

Image 3) This appears in Episode II, about halfway through the film when riding a speeder bike. This time the setting suns are at about 30&#176 and two diameters apart, except now the highest star is right of the closest star to the horizon, and not the left. The bottom star on the horizon this time is yellow not red.)

Image 4) This appears at the end of Episode III, mimicking the original movie. Interestingly the stars are again setting, but the angle is now 10&176; to the horizon and four diameters apart. Also the stars are setting at the exact same location and at the same place on the horizon. (The time is about 19 years before the original movie (Episode IV))

Image 5) This appears about 16 minutes into Episode VI at the haunt of Jabba the Hutt (and incidentally the original Salacious B. Crumb!). This time the stars are inclined at about 40° to the horizon (lowest star is to the left not right) and are spaced about eight diameters apart!

All these different directions and inclinations are confusing (and likely impossible in reality). Assuming all the evening scenes are from the approximate same latitude, I can only conclude that the orbit of the mythical planet is either inclined roughly 45— to the orbital plane of the binary star. (So the stars in the sky will always appear as double.)

Whist these stars have mostly been used for dramatic effect, it is however really hard to reconcile how these stars can vary by about 120° degrees to the local horizon from similar latitudes.

The Tatooine latitude of the storyline must be near the equator, as several different scenes show no apparent shadows during the middle of the day. (Just like the true film location in Tunisia.)

Excellent article, lots of fun, thought provoking and entertaining – A little bit of tongue-in-cheek is nice to read. However, remember that over a year ago Fraiser told all of us not to make really long comments (comments longer than the article itself) or we could get banned from UT!

I would briefly like to add that if you look at the clouds you can clearly see that there’s no ‘cosigning’ needed to flatten the image – we’re not looking through a fish bowl, so we can assume we have ~ = 35mm lense. This would suggest that the suns are indeed roughly 1 solar mass and 1AU distance (or scale factors that would produce similar angular visuals from the planet surface at a distance where water is still liquid – assuming they are water based clouds) I think the Astrophysics of this should really be looked in to. Maybe Dr. Pamela Gay could enlighten us all in another episode of Astronomy Cast – Yay! 🙂

Nice subtle comment here, mate. Write something when you know what you are talking about, and someone else always wants to silence them by stick in the knife in. According to the guide to comments here, it is actually to delete comments NOT really ban people from UT!

If you want to hear Pamela Gay, then just listen to the podcast No.152 “Binary Stars” at http://www.astronomycast.com/astronomy/ep-152-binary-stars/ (28th September 2009). (However, she thinks it is like “watching paint dry”, so I don’t know how useful her comments would be for you.) [I’m very pleased they reedited this podcast, it is a vast improvement of the information presented.]

As for the “…Astrophysics of this should really be looked in to”, the truth is that this has been for a century or more.

Planets may exist in binary configurations. I seem to recall it was not long ago it was though binary stars had no planets. Alpha Centuri has not been found to have planets. Whether such planets are biologically active is another question. I doubt the two stars can be in too close an orbit. If they start out that way it is likely their rotational angular momentum would be transferred into orbital angular momentum and they would move apart. The oscillating gravitational dipole action of the two stars would likely be fairly perturbing to planetary orbits and rattle them around a bit.

I think most likely the scenario for a binary star with a biologically active planet would be a central G-class star with a red dwarf in an orbit around or beyond the gas giants in our solar system.

“I doubt the two stars can be in too close an orbit.”
Actually, they can and stars do get this close. Such systems are the photometric or eclipsing binaries of which we know of about 3000-4000 systems. An interesting short YouTube clip as an example (Beta Persei) is athttp://www.youtube.com/watch?v=ixfQY07R-6A&feature=related This is close to the ratio of the fictional Tatooine system.)

The most distorted are the W UMa type stars, whose surfaces touch together. (However, most of these stars are relatively smaller c. 0.3 to 0.4 solar masses and are often O or B-type stars. (They do not fit the solar-like scenario, though.)

Also in close eclipsing binary systems the stars get closer over time, often because of mass loss, but all because of stellar evolution where one of the stars fills its Roche lobe when it tries to swell into a red giant. Indeed, so star are so close that they eventually merge, forming variables know as FK Comae Berenices variables (These often have rotational velocities above 100 km per second and appear ellipsoidal. They are also mostly G-type stars.)

…in a movie where people move objects with their minds, and there are planets covered in teddy bears with spears, you go on about how a 10 second scene with two setting suns is an astronomical impossibility? Dude, let it go.

I also found an interesting arXiv paper on circumstances for such systems. This lists 10 systems of interest, whose main parameters are summarised in Table 1 (pg.15).
Konacki, M. “The Radial Velocity Tatooine Search for Circumbinary Planets…” at; http://arxiv.org/abs/0908.3775

Most interesting of all is the 5.7v magnitude spectroscopic binary star 16 Psc / HIP 116495 / HD 221950 (23h 36.4m +02° 06′) that lies 32.99±0.81 (101.0±2.8 light years). According to this paper, the stars are both a solar-like F6V spectral class with rapid rotation, with the stellar masses being 1.31 and 1.24 solar masses, respectively, with a short period of 45.5 days. (Looking at the radial velocity data (pg.10), the orbit appears quite circular.)
They calculate that the optimum stable distance for planets would be 1.37AU with the period of 365 days! (This was discovered by Jocelyn Tomkin and Francis Fekel in 2008 (AJ., 135, 555 (2008)) If true, this would be very similar to the Tatooine scenario!)
From the Extrasolar Planets Encyclopaedia, no planet or planets have been found orbiting these stars.

Almost impossible but ammusing to imagine. What happens if the two stars have exactly the same mass and the the plane of revolution is exactly perpendicular to the imaginary line connecting the two stars. In this highly unrealistic case the planet can be closer to the double sun.